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An alloy of silver and gold is to be recast with an addition of silver. The alloy consists of 80 ounces, 10 ounces of which are gold. If the new alloy is to have only one-fifth of an ounce of gold in 5 ounces, how much silver must be added?
A.) 170 ounces
B.) 77 ounces
C.) 4 ounces

Respuesta :

Answer: Option 'A' is correct.

Step-by-step explanation:

Since we have given that

In 80 ounces, 10 ounces of gold.

So, Proportion of gold would be

[tex]\dfrac{10}{80}\times 100=12.5\%=0.125[/tex]

In new alloy of 5 ounces, one fifth of ounce  is gold, so, it becomes,

it means 0.2 ounce is gold in 5 ounces.

So, proportion of gold would be

[tex]\dfrac{0.2}{5}\times 100=4\%=0.04[/tex]

Let x be the amount of silver is to be added.

According to question, it becomes,

[tex]0.125\times 80=0.04(80+x)\\\\10=3.2+0.04x\\\\10-3.2=0.04x\\\\6.8=0.04x\\\\x=\dfrac{6.8}{0.04}\\\\x=170\ ounces[/tex]

Hence, Option 'A' is correct.

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